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Bug fixes and improvements (#1348)

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* Add "reference" for EN version. Bug fixes.

* Unify the figure reference as "the figure below" and "the figure above".
Bug fixes.

* Format the EN markdown files.

* Replace "" with <u></u> for EN version and bug fixes

* Fix biary_tree_dfs.png

* Fix biary_tree_dfs.png

* Fix zh-hant/biary_tree_dfs.png

* Fix heap_sort_step1.png

* Sync zh and zh-hant versions.

* Bug fixes

* Fix EN figures

* Bug fixes

* Fix the figure labels for EN version
This commit is contained in:
Yudong Jin
2024-05-06 14:44:48 +08:00
committed by GitHub
parent 8e60d12151
commit c4a7966882
99 changed files with 615 additions and 259 deletions
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8
en/docs/chapter_backtracking/backtracking_algorithm.md
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@ -8,7 +8,7 @@ Backtracking typically employs "depth-first search" to traverse the solution spa
Given a binary tree, search and record all nodes with a value of $7$, please return a list of nodes.
For this problem, we traverse this tree in preorder and check if the current node's value is $7$. If it is, we add the node's value to the result list `res`. The relevant process is shown in the following diagram and code:
For this problem, we traverse this tree in preorder and check if the current node's value is $7$. If it is, we add the node's value to the result list `res`. The relevant process is shown in the figure below:
```src
[file]{preorder_traversal_i_compact}-[class]{}-[func]{pre_order}
@ -36,7 +36,7 @@ Based on the code from Example One, we need to use a list `path` to record the v
In each "try", we record the path by adding the current node to `path`; before "retreating", we need to pop the node from `path` **to restore the state before this attempt**.
Observe the process shown below, **we can understand trying and retreating as "advancing" and "undoing"**, two operations that are reverse to each other.
Observe the process shown in the figure below, **we can understand trying and retreating as "advancing" and "undoing"**, two operations that are reverse to each other.
=== "<1>"
![Trying and retreating](backtracking_algorithm.assets/preorder_find_paths_step1.png)
@ -85,7 +85,7 @@ To meet the above constraints, **we need to add a pruning operation**: during th
[file]{preorder_traversal_iii_compact}-[class]{}-[func]{pre_order}
```
"Pruning" is a very vivid noun. As shown in the diagram below, in the search process, **we "cut off" the search branches that do not meet the constraints**, avoiding many meaningless attempts, thus enhancing the search efficiency.
"Pruning" is a very vivid noun. As shown in the figure below, in the search process, **we "cut off" the search branches that do not meet the constraints**, avoiding many meaningless attempts, thus enhancing the search efficiency.
![Pruning based on constraints](backtracking_algorithm.assets/preorder_find_constrained_paths.png)
@ -421,7 +421,7 @@ Next, we solve Example Three based on the framework code. The `state` is the nod
[file]{preorder_traversal_iii_template}-[class]{}-[func]{backtrack}
```
As per the requirements, after finding a node with a value of $7$, the search should continue, **thus the `return` statement after recording the solution should be removed**. The following diagram compares the search processes with and without retaining the `return` statement.
As per the requirements, after finding a node with a value of $7$, the search should continue, **thus the `return` statement after recording the solution should be removed**. The figure below compares the search processes with and without retaining the `return` statement.
![Comparison of retaining and removing the return in the search process](backtracking_algorithm.assets/backtrack_remove_return_or_not.png)